Ultra-finitism is not discussed much in standard philosophy of mathematics literature. In the philosophy of mathematics literature, what seems to amount to the same view is called "strict finitism". Here are four pieces on the topic:
-- a 1975 Synthese article, "Wang's Paradox", by Michael Dummett;
-- a 1982 Synthese article, "Strict Finitism", by Crispin Wright;
-- a 2005 PhD dissertation, "Strict Finitism as a Foundation for Mathematics" (University of Glasgow) by Jim Mawby; ;
-- and a 2007 Aristotelian Society article, "Strict Finitism Refuted?", by Ofra Magidor.
http://wn.com/fundamental_statement_of_prof_doron_zeilberger's_ultrafinitism/interviews?orderby=published&upload_time=today
yoo may also look at the russian schools, in Engish the works of M A Dummett dealt with it
@cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of T.Forster at dpmms.cam.ac.uk
Sent: 22 January 2013 02:25 PM
To: Foundations of Mathematics
Cc: P.T.Johnstone at dpmms.cam.ac.uk; M.Hyland at dpmms.cam.ac.uk
Subject: [FOM] Ultrafinitism - help!
I have a student here who wants to write a fourth year (Part III) essay on ultrafinitism, a topic of which my knowledge is, as it were, *ultra*finite.
Within 10 days i have to supply the faculty office a couple of paragraphs saying what the student should read and what sort of topics the essay should cover, which results should be proved, and so on.
Any enthusiasts out there who can get me out of this hole?
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